# 2D plot performance

I have this function

```
sage: f=imag(I*(sqrt(-cos(l) + 1)*cosh(sin(1/2*l)) -
sqrt(2)*sinh(sqrt(sin(1/2*l)^2)))*sin(1/2*l)^3/((-cos(l)
+ 1)^(3/2)*e^(1/2*I*l)))
```

i.m.h.o. this not something terribly complicated. I wanted to plot it. So I do

```
sage: time plot(f,l,0,10)
..nice plot..
Time: CPU 9.28 s, Wall: 9.41 s
```

**I.e. I was waiting almost 10s** for this (on an intel core duo CPU P9500 @ 2.53GHz) laptop!? I thought that maybe `fast_callable`

would help:

```
sage: ff=fast_callable(f,vars=[l],domain=CC)
sage: time plot(ff,0,10)
..same nice plot..
Time: CPU 13.24 s, Wall: 13.50 s
```

So that's even worse.
Now I compare to *Mathematica*

```
In[8]:= Timing[Plot[Im[(Sin[l/2]^3*(I*Sqrt[1 - Cos[l]]*Cosh[Sin[l/2]] -
I*Sqrt[2]*Sinh[Sqrt[Sin[l/2]^2]]))/(E^((I/2)*l)*(1 -
Cos[l])^(3/2))], {l, 0, 10}]]
Out[8]= {0.019997, ..same plot again..}
```

**~500 times faster** ... what am I doing wrong?